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Register a new userEnergy and symmetry of $dd$ excitations in undoped layered cuprates measured by Cu $L_3$ resonant inelastic x-ray scattering
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We measured high resolution Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) of the undoped cuprates La$_2$CuO$_4$, Sr$_2$CuO$_2$Cl$_2$, CaCuO$_2$ and NdBa$_2$Cu$_3$O$_6$. The dominant spectral features were assigned to $dd$ excitations and we extensively studied their polarization and scattering geometry dependence. In a pure ionic picture, we calculated the theoretical cross sections for those excitations and used them to fit the experimental data with excellent agreement. By doing so, we were able to determine the energy and symmetry of Cu-3$d$ states for the four systems with unprecedented accuracy and confidence. The values of the effective parameters could be obtained for the single ion crystal field model but not for a simple two-dimensional cluster model. The firm experimental assessment of $dd$ excitation energies carries important consequences for the physics of high $T_c$ superconductors. On one hand, having found that the minimum energy of orbital excitation is always $geq 1.4$ eV, i.e., well above the mid-infrared spectral range, leaves to magnetic excitations (up to 300 meV) a major role in Cooper pairing in cuprates. On the other hand, it has become possible to study quantitatively the effective influence of $dd$ excitations on the superconducting gap in cuprates.
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High resolution resonant inelastic x-ray scattering (RIXS) has proven particularly effective in the determination of crystal field and spin excitations in cuprates. Its strength lies in the large Cu $L_{3}$ resonance and in the fact that the scattering cross section follows quite closely the single-ion model predictions, both in the insulating parent compounds and in the superconducting doped materials. However, the spectra become increasingly broader with (hole) doping, hence resolving and assigning spectral features has proven challenging even with the highest energy resolution experimentally achievable. Here we have overcome this limitation by measuring the complete polarization dependence of the RIXS spectra as function of momentum transfer and doping in thin films of NdBa$_{2}$Cu$_{3}$O$_{7-delta}$. Besides confirming the previous assignment of $dd$ and spin excitations (magnon, bimagnon) in the antiferromagnetic insulating parent compound, we unequivocally single out the actual spin-flip contribution at all dopings. We also demonstrate that the softening of $dd$ excitations is mainly attributed to the shift of the $xy$ peak to lower energy loss. These results provide a definitive assessment of the RIXS spectra of cuprates and demonstrate that RIXS measurements with full polarization control are practically feasible and highly informative.
We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 < x < 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rather than from incoherent particle-hole excitations as recently suggested theoretically [Benjamin et al. Phys. Rev. Lett. 112, 247002(2014)]. Implications for the theoretical description of the electron system in the cuprates are discussed.
Spin excitations in the overdoped high temperature superconductors Tl$_2$Ba$_2$CuO$_{6+delta}$ and (Bi,Pb)$_2$(Sr,La)$_{2}$CuO$_{6+delta}$ were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-$L_3$ absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle/hole excitations whose maximum shows a fluorescence-like shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping.
We have performed resonant inelastic x-ray scattering (RIXS) near the Cu-K edge on cuprate superconductors La(2-x)Sr(x)CuO(4), La(2-x)Ba(x)CuO(4), La(2-x)Sr(x)Cu(1-y)Fe(y)O(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d), covering underdoped to heavily overdoped regime and focusing on charge excitations inside the charge-transfer gap. RIXS measurements of the 214 systems with Ei = 8.993 keV have revealed that the RIXS intensity at 1 eV energy transfer has a minimum at (0,0) and maxima at (0.4pi, 0) and $(0, 0.4pi) for all doping points regardless of the stripe ordered state, suggesting that the corresponding structure is not directly related to stripe order. Measurements with Ei = 9.003 keV on metallic La(1.7)Sr(0.3)CuO(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d) exhibit a dispersive intra-band excitation below 4 eV, similar to that observed in the electron-doped Nd(1.85)Ce(0.15)CuO(4). This is the first observation of a dispersive intra-band excitation in a hole doped system, evidencing that both electron and hole doped systems have a similar dynamical charge correlation function.
We present calculations for resonant inelastic x-ray scattering (RIXS) in edge-shared copper oxide systems, such as CuGeO$_{3}$ and Li$_{2}$CuO$_{2}$, appropriate for hard x-ray scattering where the photoexcited electron lies above oxygen 2p and copper 3d orbital energies. We perform exact diagonalizations of the multi-band Hubbard and determine the energies, orbital character and resonance profiles of excitations which can be probed via RIXS. We find excellent agreement with recent results on Li$_{2}$CuO$_{2}$ and CuGeO$_{3}$ in the 2-7 eV photon energy loss range.
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